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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 19 Oct 2009 01:48:08 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t1255938526d2l9ijr1k8ujt8q.htm/, Retrieved Mon, 29 Apr 2024 17:42:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47574, Retrieved Mon, 29 Apr 2024 17:42:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCentral Tendency Part 2.3
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3] [2009-10-19 07:48:08] [eeda0e496238f8886c14dbbeff6ff613] [Current]
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Dataseries X:
0.806451613
0.819277108
0.8125
0.776470588
0.730769231
0.720720721
0.743119266
0.77
0.815217391
0.826086957
0.821052632
0.8125
0.821052632
0.824175824
0.842696629
0.788888889
0.742574257
0.72815534
0.745098039
0.802083333
0.836956522
0.849462366
0.861702128
0.872340426
0.891304348
0.911111111
0.877777778
0.811111111
0.704081633
0.66
0.683673469
0.741935484
0.777777778
0.788888889
0.791208791
0.78021978
0.758241758
0.760869565
0.772727273
0.771084337
0.797619048
0.814814815
0.831168831
0.797468354
0.784810127
0.8125
0.860759494
0.894736842
0.901408451
0.897058824
0.892307692
0.884057971
0.87804878
0.83908046
0.831325301
0.772151899
0.773333333
0.794871795
0.855421687
0.916666667
0.963414634




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47574&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47574&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.810563770524590.00775112424751829104.573703715833
Geometric Mean0.808326844206217
Harmonic Mean0.806073591386973
Quadratic Mean0.812784363600253
Winsorized Mean ( 1 / 20 )0.8101855000655740.00741453937543357109.26983579721
Winsorized Mean ( 2 / 20 )0.8106724708196720.00719358454090267112.693812967679
Winsorized Mean ( 3 / 20 )0.811013606622950.00689526954798759117.618840130717
Winsorized Mean ( 4 / 20 )0.8112159011803280.00673041004098568120.529937439224
Winsorized Mean ( 5 / 20 )0.8112398281475410.00664660088507875122.053338567196
Winsorized Mean ( 6 / 20 )0.8120992153278690.00638498094455527127.188980261621
Winsorized Mean ( 7 / 20 )0.8120573793114750.00634754962738783127.932419119290
Winsorized Mean ( 8 / 20 )0.8111785113770490.00614149764402295132.081547269909
Winsorized Mean ( 9 / 20 )0.8105838595409840.00591560295631463137.024723519641
Winsorized Mean ( 10 / 20 )0.8126941410163930.0055307338474352146.941466256466
Winsorized Mean ( 11 / 20 )0.8121875017540980.00526375144212342154.298224504776
Winsorized Mean ( 12 / 20 )0.8118908729672130.00459143553482176176.827239936133
Winsorized Mean ( 13 / 20 )0.8119210719672130.0045202171502648179.619926427572
Winsorized Mean ( 14 / 20 )0.8109410157377050.00426636038087593190.077945448014
Winsorized Mean ( 15 / 20 )0.8096170943442620.00399547781446936202.633359998218
Winsorized Mean ( 16 / 20 )0.8080014413606560.00368368996288107219.345669560287
Winsorized Mean ( 17 / 20 )0.807867973524590.00339114378421786238.228758475046
Winsorized Mean ( 18 / 20 )0.8076269659180330.00323631213448954249.551629248339
Winsorized Mean ( 19 / 20 )0.8066336026229510.00286028970211594282.011155033083
Winsorized Mean ( 20 / 20 )0.8080873327868850.00262563646063709307.768171603927
Trimmed Mean ( 1 / 20 )0.8105250062372880.00712786304859417113.712202480819
Trimmed Mean ( 2 / 20 )0.8108883374035090.00677453583659811119.696516036249
Trimmed Mean ( 3 / 20 )0.8110080452363640.00648857206427615124.990219296707
Trimmed Mean ( 4 / 20 )0.8110059116226420.00628073345685371129.125987783743
Trimmed Mean ( 5 / 20 )0.8109431206274510.00608592393071557133.248974167198
Trimmed Mean ( 6 / 20 )0.8108692465102040.00586840493194659138.175408124271
Trimmed Mean ( 7 / 20 )0.8106031894255320.00567429163677714142.85539787411
Trimmed Mean ( 8 / 20 )0.81032158440.00543403968347083149.119555910646
Trimmed Mean ( 9 / 20 )0.8101696293255810.00518285783101277156.317162411393
Trimmed Mean ( 10 / 20 )0.8101011522439020.00491827827847069164.712345738964
Trimmed Mean ( 11 / 20 )0.8096955822051280.00467534225640072173.184237174642
Trimmed Mean ( 12 / 20 )0.8093221004054050.00442498888526491182.898109213432
Trimmed Mean ( 13 / 20 )0.8089490167714290.00427878241019481189.060564249304
Trimmed Mean ( 14 / 20 )0.8085264168484850.00408973005722191197.696768621865
Trimmed Mean ( 15 / 20 )0.8081870377419350.00389881419177223207.290472946229
Trimmed Mean ( 16 / 20 )0.8079865010689660.00370967407626305217.805253091908
Trimmed Mean ( 17 / 20 )0.8079843914444440.00353429482651139228.61261753932
Trimmed Mean ( 18 / 20 )0.808001100840.00336866891543496239.857677059864
Trimmed Mean ( 19 / 20 )0.8080562270.0031612846379668255.610082463092
Trimmed Mean ( 20 / 20 )0.8082737209523810.00298388993560933270.879200772976
Median0.8125
Midrange0.811707317
Midmean - Weighted Average at Xnp0.806811193466667
Midmean - Weighted Average at X(n+1)p0.808187037741936
Midmean - Empirical Distribution Function0.808187037741936
Midmean - Empirical Distribution Function - Averaging0.808187037741936
Midmean - Empirical Distribution Function - Interpolation0.808187037741936
Midmean - Closest Observation0.80706093965625
Midmean - True Basic - Statistics Graphics Toolkit0.808187037741936
Midmean - MS Excel (old versions)0.808187037741936
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.81056377052459 & 0.00775112424751829 & 104.573703715833 \tabularnewline
Geometric Mean & 0.808326844206217 &  &  \tabularnewline
Harmonic Mean & 0.806073591386973 &  &  \tabularnewline
Quadratic Mean & 0.812784363600253 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.810185500065574 & 0.00741453937543357 & 109.26983579721 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.810672470819672 & 0.00719358454090267 & 112.693812967679 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.81101360662295 & 0.00689526954798759 & 117.618840130717 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.811215901180328 & 0.00673041004098568 & 120.529937439224 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.811239828147541 & 0.00664660088507875 & 122.053338567196 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.812099215327869 & 0.00638498094455527 & 127.188980261621 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.812057379311475 & 0.00634754962738783 & 127.932419119290 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.811178511377049 & 0.00614149764402295 & 132.081547269909 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.810583859540984 & 0.00591560295631463 & 137.024723519641 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.812694141016393 & 0.0055307338474352 & 146.941466256466 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.812187501754098 & 0.00526375144212342 & 154.298224504776 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.811890872967213 & 0.00459143553482176 & 176.827239936133 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.811921071967213 & 0.0045202171502648 & 179.619926427572 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.810941015737705 & 0.00426636038087593 & 190.077945448014 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.809617094344262 & 0.00399547781446936 & 202.633359998218 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.808001441360656 & 0.00368368996288107 & 219.345669560287 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.80786797352459 & 0.00339114378421786 & 238.228758475046 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.807626965918033 & 0.00323631213448954 & 249.551629248339 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.806633602622951 & 0.00286028970211594 & 282.011155033083 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.808087332786885 & 0.00262563646063709 & 307.768171603927 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.810525006237288 & 0.00712786304859417 & 113.712202480819 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.810888337403509 & 0.00677453583659811 & 119.696516036249 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.811008045236364 & 0.00648857206427615 & 124.990219296707 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.811005911622642 & 0.00628073345685371 & 129.125987783743 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.810943120627451 & 0.00608592393071557 & 133.248974167198 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.810869246510204 & 0.00586840493194659 & 138.175408124271 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.810603189425532 & 0.00567429163677714 & 142.85539787411 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.8103215844 & 0.00543403968347083 & 149.119555910646 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.810169629325581 & 0.00518285783101277 & 156.317162411393 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.810101152243902 & 0.00491827827847069 & 164.712345738964 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.809695582205128 & 0.00467534225640072 & 173.184237174642 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.809322100405405 & 0.00442498888526491 & 182.898109213432 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.808949016771429 & 0.00427878241019481 & 189.060564249304 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.808526416848485 & 0.00408973005722191 & 197.696768621865 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.808187037741935 & 0.00389881419177223 & 207.290472946229 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.807986501068966 & 0.00370967407626305 & 217.805253091908 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.807984391444444 & 0.00353429482651139 & 228.61261753932 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.80800110084 & 0.00336866891543496 & 239.857677059864 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.808056227 & 0.0031612846379668 & 255.610082463092 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.808273720952381 & 0.00298388993560933 & 270.879200772976 \tabularnewline
Median & 0.8125 &  &  \tabularnewline
Midrange & 0.811707317 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.806811193466667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.808187037741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.808187037741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.808187037741936 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.808187037741936 &  &  \tabularnewline
Midmean - Closest Observation & 0.80706093965625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.808187037741936 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.808187037741936 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47574&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.81056377052459[/C][C]0.00775112424751829[/C][C]104.573703715833[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.808326844206217[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.806073591386973[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.812784363600253[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.810185500065574[/C][C]0.00741453937543357[/C][C]109.26983579721[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.810672470819672[/C][C]0.00719358454090267[/C][C]112.693812967679[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.81101360662295[/C][C]0.00689526954798759[/C][C]117.618840130717[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.811215901180328[/C][C]0.00673041004098568[/C][C]120.529937439224[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.811239828147541[/C][C]0.00664660088507875[/C][C]122.053338567196[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.812099215327869[/C][C]0.00638498094455527[/C][C]127.188980261621[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.812057379311475[/C][C]0.00634754962738783[/C][C]127.932419119290[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.811178511377049[/C][C]0.00614149764402295[/C][C]132.081547269909[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.810583859540984[/C][C]0.00591560295631463[/C][C]137.024723519641[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.812694141016393[/C][C]0.0055307338474352[/C][C]146.941466256466[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.812187501754098[/C][C]0.00526375144212342[/C][C]154.298224504776[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.811890872967213[/C][C]0.00459143553482176[/C][C]176.827239936133[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.811921071967213[/C][C]0.0045202171502648[/C][C]179.619926427572[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.810941015737705[/C][C]0.00426636038087593[/C][C]190.077945448014[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.809617094344262[/C][C]0.00399547781446936[/C][C]202.633359998218[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.808001441360656[/C][C]0.00368368996288107[/C][C]219.345669560287[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.80786797352459[/C][C]0.00339114378421786[/C][C]238.228758475046[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.807626965918033[/C][C]0.00323631213448954[/C][C]249.551629248339[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.806633602622951[/C][C]0.00286028970211594[/C][C]282.011155033083[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.808087332786885[/C][C]0.00262563646063709[/C][C]307.768171603927[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.810525006237288[/C][C]0.00712786304859417[/C][C]113.712202480819[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.810888337403509[/C][C]0.00677453583659811[/C][C]119.696516036249[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.811008045236364[/C][C]0.00648857206427615[/C][C]124.990219296707[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.811005911622642[/C][C]0.00628073345685371[/C][C]129.125987783743[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.810943120627451[/C][C]0.00608592393071557[/C][C]133.248974167198[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.810869246510204[/C][C]0.00586840493194659[/C][C]138.175408124271[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.810603189425532[/C][C]0.00567429163677714[/C][C]142.85539787411[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.8103215844[/C][C]0.00543403968347083[/C][C]149.119555910646[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.810169629325581[/C][C]0.00518285783101277[/C][C]156.317162411393[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.810101152243902[/C][C]0.00491827827847069[/C][C]164.712345738964[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.809695582205128[/C][C]0.00467534225640072[/C][C]173.184237174642[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.809322100405405[/C][C]0.00442498888526491[/C][C]182.898109213432[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.808949016771429[/C][C]0.00427878241019481[/C][C]189.060564249304[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.808526416848485[/C][C]0.00408973005722191[/C][C]197.696768621865[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.808187037741935[/C][C]0.00389881419177223[/C][C]207.290472946229[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.807986501068966[/C][C]0.00370967407626305[/C][C]217.805253091908[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.807984391444444[/C][C]0.00353429482651139[/C][C]228.61261753932[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.80800110084[/C][C]0.00336866891543496[/C][C]239.857677059864[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.808056227[/C][C]0.0031612846379668[/C][C]255.610082463092[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.808273720952381[/C][C]0.00298388993560933[/C][C]270.879200772976[/C][/ROW]
[ROW][C]Median[/C][C]0.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.811707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.806811193466667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.808187037741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.808187037741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.808187037741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.808187037741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.80706093965625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.808187037741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.808187037741936[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47574&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.810563770524590.00775112424751829104.573703715833
Geometric Mean0.808326844206217
Harmonic Mean0.806073591386973
Quadratic Mean0.812784363600253
Winsorized Mean ( 1 / 20 )0.8101855000655740.00741453937543357109.26983579721
Winsorized Mean ( 2 / 20 )0.8106724708196720.00719358454090267112.693812967679
Winsorized Mean ( 3 / 20 )0.811013606622950.00689526954798759117.618840130717
Winsorized Mean ( 4 / 20 )0.8112159011803280.00673041004098568120.529937439224
Winsorized Mean ( 5 / 20 )0.8112398281475410.00664660088507875122.053338567196
Winsorized Mean ( 6 / 20 )0.8120992153278690.00638498094455527127.188980261621
Winsorized Mean ( 7 / 20 )0.8120573793114750.00634754962738783127.932419119290
Winsorized Mean ( 8 / 20 )0.8111785113770490.00614149764402295132.081547269909
Winsorized Mean ( 9 / 20 )0.8105838595409840.00591560295631463137.024723519641
Winsorized Mean ( 10 / 20 )0.8126941410163930.0055307338474352146.941466256466
Winsorized Mean ( 11 / 20 )0.8121875017540980.00526375144212342154.298224504776
Winsorized Mean ( 12 / 20 )0.8118908729672130.00459143553482176176.827239936133
Winsorized Mean ( 13 / 20 )0.8119210719672130.0045202171502648179.619926427572
Winsorized Mean ( 14 / 20 )0.8109410157377050.00426636038087593190.077945448014
Winsorized Mean ( 15 / 20 )0.8096170943442620.00399547781446936202.633359998218
Winsorized Mean ( 16 / 20 )0.8080014413606560.00368368996288107219.345669560287
Winsorized Mean ( 17 / 20 )0.807867973524590.00339114378421786238.228758475046
Winsorized Mean ( 18 / 20 )0.8076269659180330.00323631213448954249.551629248339
Winsorized Mean ( 19 / 20 )0.8066336026229510.00286028970211594282.011155033083
Winsorized Mean ( 20 / 20 )0.8080873327868850.00262563646063709307.768171603927
Trimmed Mean ( 1 / 20 )0.8105250062372880.00712786304859417113.712202480819
Trimmed Mean ( 2 / 20 )0.8108883374035090.00677453583659811119.696516036249
Trimmed Mean ( 3 / 20 )0.8110080452363640.00648857206427615124.990219296707
Trimmed Mean ( 4 / 20 )0.8110059116226420.00628073345685371129.125987783743
Trimmed Mean ( 5 / 20 )0.8109431206274510.00608592393071557133.248974167198
Trimmed Mean ( 6 / 20 )0.8108692465102040.00586840493194659138.175408124271
Trimmed Mean ( 7 / 20 )0.8106031894255320.00567429163677714142.85539787411
Trimmed Mean ( 8 / 20 )0.81032158440.00543403968347083149.119555910646
Trimmed Mean ( 9 / 20 )0.8101696293255810.00518285783101277156.317162411393
Trimmed Mean ( 10 / 20 )0.8101011522439020.00491827827847069164.712345738964
Trimmed Mean ( 11 / 20 )0.8096955822051280.00467534225640072173.184237174642
Trimmed Mean ( 12 / 20 )0.8093221004054050.00442498888526491182.898109213432
Trimmed Mean ( 13 / 20 )0.8089490167714290.00427878241019481189.060564249304
Trimmed Mean ( 14 / 20 )0.8085264168484850.00408973005722191197.696768621865
Trimmed Mean ( 15 / 20 )0.8081870377419350.00389881419177223207.290472946229
Trimmed Mean ( 16 / 20 )0.8079865010689660.00370967407626305217.805253091908
Trimmed Mean ( 17 / 20 )0.8079843914444440.00353429482651139228.61261753932
Trimmed Mean ( 18 / 20 )0.808001100840.00336866891543496239.857677059864
Trimmed Mean ( 19 / 20 )0.8080562270.0031612846379668255.610082463092
Trimmed Mean ( 20 / 20 )0.8082737209523810.00298388993560933270.879200772976
Median0.8125
Midrange0.811707317
Midmean - Weighted Average at Xnp0.806811193466667
Midmean - Weighted Average at X(n+1)p0.808187037741936
Midmean - Empirical Distribution Function0.808187037741936
Midmean - Empirical Distribution Function - Averaging0.808187037741936
Midmean - Empirical Distribution Function - Interpolation0.808187037741936
Midmean - Closest Observation0.80706093965625
Midmean - True Basic - Statistics Graphics Toolkit0.808187037741936
Midmean - MS Excel (old versions)0.808187037741936
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')